An approach to discovering the low-energy space for effective quantum models of realistic systems.

Low-energy effective models can be powerful tools for understanding realistic systems, but in many cases it is difficult to quantify the accuracy of those models for a specific system. Density matrix downfolding (DMD) [1] is one approach to determining accurate effective models from first-principles many-body calculations, but requires a sample of low-energy wave functions with varying properties. We present a new method, constrained variational Monte Carlo, which targets low-energy wave functions while varying other properties, such as the average double-occupation of orbitals. We tested the approach on the hydrogen molecule at stretched and compressed bond lengths, and use it to explore how the low-energy space changes with bond length. For example, when the bond is stretched the low-energy space shifts such that interactions become necessary to accurately describe it. Models fitted to the generated states were solved and reproduced the exact low-energy spectrum of the first-principles Hamiltonian. The method provides a systematic many-body approach to exploring the low-energy space of realistic systems. [1] Changlani et al., J. Chem. Phys., 143, 10, 102814, (2015).